A group that claims to represent the rights of atheists in Ireland has launched a campaign to expel God from the Irish constitution, starting with an attempt to block plans for a new blasphemy law.

Atheist Ireland, which is led by a Bono impersonator and the writer of a hit musical about Roy Keane's infamous World Cup tantrum, says the proposed legislation combines the oppressive religious thinking of 1950s Catholic Ireland and Islamic fundamentalism.

Co-founder Michael Nugent said they intended to launch a roadshow in the republic to kick-start their campaign.

Nugent is the co-author of I, Keano, a comedy musical about the angry clash between Keane and former Ireland manager Mick McCarthy at the 2002 World Cup, which led to Keane walking out of the tournament. He has been joined by Paul Wonderful, a former singer with U2 send-up band The Joshua Trio, whose current incarnation - Ding Dong Denny O'Reilly - sings a song about Christ that could be illegal under the new law.

Dermot Ahern, Ireland's justice minister, has proposed the legislation, which will outlaw anything seen as "grossly abusive or insulting in relation to matters held sacred by any religion, thereby causing outrage among a substantial number of the adherents of that religion". The legislation also includes fines of up to €100,000 for "blasphemous libel", a move that Nugent and Atheist Ireland describe as "criminalising free speech".

"This new law will treat religious beliefs as more valuable than secular beliefs and scientific thinking," Nugent said. He said the real solution to dealing with Ireland's current blasphemy law was to remove all references to religion in the 1937 constitution.

"The bill's first test of blasphemy is that religious adherents express outrage. Instead of encouraging outrage, we should be educating people to respond in a more healthy manner when somebody expresses a belief that they find insulting," Nugent said. "More worryingly, this law would encourage the type of orchestrated outrage that Islamic fundamentalists directed against Danish cartoonists."

The Dublin-based writer said many atheists found parts of the Bible insulting, but would not wish it to be banned or discussion about it closed down. "Parts of the Christian Bible suggest that women must not teach and must learn in silence, or that effeminate people are unrighteous, or that people should worship a god who threatens to make you eat your own children. But we do not believe the Bible should be banned, and neither should discussion of the Bible in terms that cause Christians to be outraged," said Nugent.

Under the proposed law, Ding Dong Denny O'Reilly, a spoof Irish republican extremist who sings in a Celtic shirt, could be prosecuted for his song The Ballad of Jaysus Christ, Nugent said.

Atheist Ireland's campaign against the proposed blasphemy law has been backed by Index on Censorship, the global campaign group for freedom of expression. Padraig Reidy, Index's news editor, said: "Ireland's ethnic and religious make-up has changed dramatically in the last 15 years. If the country is to thrive, surely the state must create a space where we can talk more, and more vigorously, about our beliefs and ideals, rather than shut down conversation."

Nugent said blasphemy was not the only anomaly in the constitution. "You cannot become president of Ireland or be appointed a judge in the republic unless you take a religious oath asking God to direct and sustain you in your work.

"What an atheist is offered is an Irish solution - to ignore it, to pretend you believe in God. But this means, for example, that a new judge who is privately an atheist but swears to God is technically committing perjury.

"We should be amending our constitution to remove these theistic references, not creating new crimes to enforce provisions that were written in the 1930s," he added.